#### Measurement of Temperature, Physics tutorial

Temperature (T) is states as degree of hotness or coldness of body. Temperature is one of the seven SI base quantities and it is estimate in Kelvin (K). Temperature of the body has no upper limit but it has lower limit (absolute zero or zero Kelvin)

Heat (Q) is the form of energy which is transferred from one part of substance to another or from one body to another by virtue of difference in temperature (that is temperature gradient). Unit of heat is in Joules (J).

Sign of heat (Q):

Q is positive when there is flow of heat in system. Q is negative when there is flow of heat out of system

Temperature and Heat:

Temperature is a degree of hotness or coldness of the body. Heat, on the other hand, is the form of energy which flows from the body of higher temperature to the body of lower temperature. From definition of heat, it is clear that temperature gradient provides direction of heat flow (i.e. from the body of higher temperature to the body of lower temperature). Procedure of heat flow is known as heat exchange. For two bodies in thermal contact, this procedure of heat exchange will continue until two bodies achieved thermal equilibrium (i.e. equal temperature). For example, in figure (a) given below the temperature of system is greater than that of surroundings, so heat flows out of system ( - Q ). In (b) temperature of the system Ts is less than that of surrounding, so heat flow in system (+ Q ). In (c) temperature of system and that of surrounding Te are equal (that is they are in thermal equilibrium), therefore no flow of heat (Q = 0).

Zeroth Law of Thermodynamics:

Assume one of the two bodies is in thermal contact with third body, after a short time thermal equilibrium will be attained between the two bodies. Assume body B is in thermal contact with bodies A and C but bodies A and C are not in thermal contact. If B is in thermal equilibrium with each of A and C, then A and C are in thermal equilibrium.

Zeroth Law of thermodynamics defines that if bodies A and C are each in thermal equilibrium with the third body B, then they are in thermal equilibrium with each other.

Temperature Scales:

Available temperature scales are; Celsius scale (also called as Centigrade scale), the Kelvin scale, the the Fahrenheit scale, Rankine scale, and te international thermodynamic temperature scale

Triple Point of Water:

In setting up the temperature scale, there is need to choose some reproducible thermal phenomenon and, fairly arbitrarily, allot a certain Kelvin temperature to environment; that is, we choose the standard fixed point and give it a standard fixed-point temperature. Triple point of water is the temperature at which solid ice, liquid water, and water vapor coexist in thermal equilibrium at same temperature and pressure. By international convention, triple point of water is 273.16 K and this value is the standard fixed-point temperature (T3 ) for calibration of thermometers.

T3 = 273.16K

Other fixed-point temperatures in addition with T3 are boiling point of water, and absolute zero temperature. The boiling point of water is 1000C whereas absolute zero temperature (0 K) is all gases have zero volume.

Conversion between Temperature Scales:

There is possibility of changing from one temperature scale to another. The conversion formulas are listed below.

Kelvin Scale to Celsius Temperature Scale

The relation between Kelvin scale and Celsius scale is

Tc = (T - 273.15)0C

Where Tc is the temperature in degree centigrade, and T is the temperature in Kelvin.

Kelvin Temperature scale

The relation between Celsius scale and Kelvin scale is

T = (Tc + 273.15)K,

Where Tc is temperature in degree centigrade, and T is temperature in Kelvin.

Fahrenheit Temperature scale

The relation between Celsius scale and Fahrenheit scale is

TF = 9/5Tc - 32

Where Tc is the temperature in degree centigrade, and TF is the temperature in Fahrenheit.

Thermometers:

Thermometers are instruments which are utilized to compute temperature of the body or system.

Thermometric Properties:

It has been seen experimentally that properties of numerous bodies or objects change with temperature. Examples of such properties are volume of liquid, length of metal rod, and electrical resistance of the wire. These properties of material can be utilized as basis of the instrument to compute temperature and they are known as Thermometric Properties.

Calibration:

Usually, calibration is the procedure of comparing output value an instrument is given with that of standard instrument (i.e. one that its output is known to be true or correct value). From this procedure, adjustment can then be made to instrument to be calibrated to give correct output. When this is done, instrument is expressed as calibrated.

Method being used in calibrating thermometers is to use device to compute easily reproducible temperatures like triple point of water and boiling point of water. If thermometric property being utilized is recorded at these two temperatures, linear graph can be plotted using the two set of variables. From this graph, the linear relationship can be attained between temperature and thermometric property.

In another way, one can compute thermometric property, say X , when thermometer is placed in contact with system or body which temperature is to be estimated. Then we have

T(X) = aX

Where TX is temperature of body to be estimated, a is a constant, and X is value of thermometric property at TX. It also applies when thermometer is placed in contact with simply reproducible temperature. Triple point of water is generally utilized. Then we have

T3 = 273.16K = aX3

So we get

a = 273.16K/X3

By solving equation we get

T(X) = (273.16K)X/X3

This equation is generally applicable to all thermometers.

Kinds of Thermometers:

Three kinds of thermometer are given below.

Thermocouple Thermometer:

It has been seen that when two dissimilar metals are joined together to make two junctions, electromotive force (emf) will flow in circuit. This emf can be estimated using the voltmeter and its value depends on temperature difference between junctions. Arrangement is known as thermocouple and observation is called as Seebeck effect. Thermocouple thermometer is based on Seebeck effect.

Thermometric property: emf generated when two junctions made from two different metals are maintained at different temperature. Test junction is placed on body or inside system whose temperature is to be computed, while reference junction is maintained at constant temperature at 00C. Potentiometer is connected to terminals to voltmeter. Relationship between emf and temperature is

emf = a + bT + cT2 + dT3

Where a, b, c, and d are constant and they are different for each thermocouple. Equation can also written as:

T(emf) = (273.16K)emf/emf3

Range of measurement of thermocouple thermometer depends on choice of metals utilized. For instance, a platinum-10 % rhodium/platinum thermocouple has temperature range of 0 to 16000C. Thermocouple thermometer is utilized widely in scientific laboratories.

Resistance Thermometer:

Electrical conductivity of the metal depends on movement of electrons through crystal lattice. Electrical resistance of the conductor, because of thermal excitation, differs with temperature. This forms basic principle of operation of resistance thermometer Resistance thermometer thus, uses variation in electrical conductivity of a conductor to indicate temperature.

The relationship between the temperature and the electrical resistance is usually non-linear and described by a higher order polynomial:

R(T) = R0(1 + AT + BT2 + CT3 +.....)

Where T is Celsius temperature, Ro is nominal resistance at the specified temperature, and A, B, C are constants. Number of higher order terms considered is the function of required accuracy of measurement. Constants (i.e. A, B and C etc.) depend on conductor material utilized and essentially describe temperature-resistance relationship. Value Ro is referred to as nominal value or nominal resistance and is resistance at 0°C. Material most usually utilized for resistance thermometers are Platinum, Copper and Nickel. Though, Platinum is most dominant material internationally. Calibration of this instrument needs measurement of R(T) at different known temperatures and from these constants in equation can be obtained. Though, equation can be utilized to obtained

T(R) = (273.16K)R/R3

Constant-Volume Gas Thermometer:

Constant-Volume gas thermometer is usually referred to as standard thermometer and is generally utilized to calibrate other thermometers. Working principle is based on pressure of the gas in the fixed volume. Constant-volume gas thermometer comprises of the gas-filled bulb connected by the tube to the mercury manometer. By raising and lowering reservoir R, mercury level on left can always be brought to zero of scale to keep gas volume constant.

The basic equation is

P = P0 - Ρgh

Where Po is atmospheric pressure, Ρ is density of mercury in manometer, g is the acceleration because of gravity, and h is estimated difference between mercury levels in two arms of tube.

Difference in height h between two arms of the manometer can be estimated when gas filled bulb is surrounded by system which temperature is to be estimated, and when it is surrounded with water at triple point. Using equation relationship between temperature and pressure of gas is

T(P) = (273.16K)(P/P3)

Where T(P) is temperature of system which temperature is to be estimated, P is pressure of gas at that temperature, and P3 is pressure at triple point of water.

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